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Name
Date
Class Period
Grade
/30
Central Net Force Model Worksheet 2/3:
Radial Net Force
1. a. A car travels through a valley at constant speed, though not at constant velocity. Explain
how this is possible.
b. Construct a qualitative motion map for the car.
c. Is the car accelerating? What direction is the car's acceleration? (Explain how you know.)
d. Construct a qualitative force diagram for the car at the moment it is at the bottom of the
valley. Are the forces balanced? Justify the relative sizes of the forces.
e. If the car's speed is 25 m/s, its mass is 1200 kg and the radius of valley (r) is 25 meters,
determine the magnitude of the centripetal force acting on the car.
f. Construct a quantitative force diagram for the car
at the bottom of the valley.
2. A car travels over a hill at constant speed.
a. Construct a qualitative motion map for the car.
b. Is the car accelerating? What direction is the car's acceleration? (Explain how you
know.)
c. If the speed of the car is 43 km/h, its mass is 1200 kg and the radius of the hill (r) is
25m, determine the magnitude of the centripetal force acting on the car.
d. Construct a quantitative force diagram for the car at the moment it is at the top of the
hill. Are the forces balanced? Justify the relative sizes of the forces.
3. Roads are banked (tilted) in curves in order to make turning a car at high speeds safer.
a. For the situation of an unbanked road, draw a force diagram for a car coming toward
you as it is turning. Which force provides the force needed to make the turn?
b. For the situation of a banked road, draw a force diagram for a car coming toward you
as it is turning. Identify all of the forces and components of forces that contribute to the
force needed to make the turn.
4. A yo-yo pro swings the yo-yo "around the world." Draw force diagrams for the yo-yo at each
of the four positions shown: top, descending side, bottom, ascending side. For each of the
positions, indicate which force or combination of forces provides the force needed for
circular motion.
5. A woman flying aerobatics executes a maneuver as illustrated below. Construct a quantitative
force diagram of all relevant forces acting on the woman flying the airplane when upside-down
at the top of the loop.
r = 380 m
v = 235 km/hr
pilot mass = 55 kg
6. Six children run on a track with equal speeds. Their masses are expressed in multiples of mass
“M” and their path radii are expressed in multiples of radius “R.”
a. Rank the centripetal acceleration of the lettered children
from largest to smallest. (Ties are possible.)
D 2M
E
largest -> ____ ____ ____ ____ ____ ____ <-smallest
Explain how you determined your ranking:
4R
F
2M
3M
5R
A 4M
B M
6R
C 6M
b. Rank the centripetal force needed for each child to remain in circular motion. (Ties are
possible.)
largest -> ____ ____ ____ ____ ____ ____ <-smallest
Explain how you determined your ranking:
7. Rollercoasters use a hill for riders to gain speed followed by an upside down loop. The loops
are designed with large radius bottoms and small radius tops, and such a shape is called a
clothoid. Answer the following questions in order to find out why the clothoid is used.
The speed of the rollercoaster is 22 m/s at
the bottom of the loop and 8 m/s at the top
of the loop.
a. Use quantitative force diagrams
to determine the size of the force on
the rider by the seat at the top and
bottom of the loop.
b. Now suppose the rollercoaster had been designed with the small 5 meter radius at the
bottom and the large 10 meter radius at the top. Use quantitative force diagrams to
determine the size of the force on the rider by the seat at the top and bottom of the loop.
c. Why is the clothoid shape used in rollercoasters?
8. 80 kg Tarzan grabs a vine to swing to another tree.
a. As Tarzan swings from point A to point B, describe qualitatively how the tension in the
vine changes and why.
8m
A
2m
BC
b. At point B he is swinging at 7 m/s and the vine is 8 meters long. How hard does he
have to hang on to the vine to keep from slipping off?
c. A moment later, at point C, the vine catches on a branch, reducing the radius of the
swing to 2 m. If Tarzan is still traveling at 7 m/s, how hard does he now have to hold on
to the vine?
d. If Tarzan slips off at point C what will be the path he takes? (Sketch the path on the
diagram.) How does this path differ from circular motion?
9. Six children of equal masses run on a track. Their speeds are expressed in multiples of
velocity “V” and their path radii are expressed in multiples of radius “R.”
a. Rank the centripetal acceleration of the lettered children
from largest to smallest. (Ties are possible.)
E
largest -> ____ ____ ____ ____ ____ ____ <-smallest
Explain how you determined your ranking:
4R
3V
5R
A 4V
B V
b. Rank the centripetal force needed for each child to remain
in circular motion. (Ties are possible.)
F
2V
D 2V
6R
C 6V
largest -> ____ ____ ____ ____ ____ ____ <-smallest
Explain how you determined your ranking:
10. An amusement park ride operates as follows: riders enter the cylindrical structure when it is
stationary with the floor at the point marked "a". They then stand against the wall as the cylinder
then begins to rotate. When it is up to speed, the floor is lowered to the position marked "b",
leaving the riders "suspended" against the wall high above the floor.
Determine the period of rotation necessary to keep the riders from sliding down the wall when
the floor is lowered from point "a" to point "b". (Show all of your work and explain your
reasoning.)